The eight planets of the Solar System arranged in order from the sun:
Mercury: 46 million km / 29 million miles (.307 AU)
Venus: 107 million km / 66 million miles (.718 AU)
Earth: 147 million km / 91 million miles (.98 AU)
Mars: 205 million km / 127 million miles (1.38 AU)
Jupiter: 741 million km /460 million miles (4.95 AU)
Saturn: 1.35 billion km / 839 million miles (9.05 AU)
Uranus: 2.75 billion km / 1.71 billion miles (18.4 AU)
Neptune: 4.45 billion km / 2.77 billion miles (29.8 AU)
Astronomers often use a term called astronomical unit (AU) to represent the distance from the Earth to the Sun.
+ Pluto (Dwarf Planet): 4.44 billion km / 2.76 billion miles (29.7 AU)
Answer:
a The kinetic energy is ![KE = 0.0543 J](https://tex.z-dn.net/?f=KE%20%3D%200.0543%20J)
b The height of the center of mass above that position is
Explanation:
From the question we are told that
The length of the rod is ![L = 1.4m](https://tex.z-dn.net/?f=L%20%3D%201.4m)
The mass of the rod
The angular speed at the lowest point is ![w = 1.09 \ rad/s](https://tex.z-dn.net/?f=w%20%3D%201.09%20%5C%20rad%2Fs)
Generally moment of inertia of the rod about an axis that passes through its one end is
Substituting values
![I = \frac{(0.140) (1.4)^2}{3}](https://tex.z-dn.net/?f=I%20%3D%20%5Cfrac%7B%280.140%29%20%281.4%29%5E2%7D%7B3%7D)
![I = 0.0915 \ kg \cdot m^2](https://tex.z-dn.net/?f=I%20%3D%200.0915%20%5C%20kg%20%5Ccdot%20m%5E2)
Generally the kinetic energy rod is mathematically represented as
![KE = \frac{1}{2} Iw^2](https://tex.z-dn.net/?f=KE%20%3D%20%5Cfrac%7B1%7D%7B2%7D%20Iw%5E2)
![KE = \frac{1}{2} (0.0915) (1.09)^2](https://tex.z-dn.net/?f=KE%20%3D%20%5Cfrac%7B1%7D%7B2%7D%20%280.0915%29%20%281.09%29%5E2)
![KE = 0.0543 J](https://tex.z-dn.net/?f=KE%20%3D%200.0543%20J)
From the law of conservation of energy
The kinetic energy of the rod during motion = The potential energy of the rod at the highest point
Therefore
![KE = PE = mgh](https://tex.z-dn.net/?f=KE%20%3D%20PE%20%3D%20mgh)
![0.0543 = mgh](https://tex.z-dn.net/?f=0.0543%20%3D%20mgh)
![h = \frac{0.0543}{9.8 * 0.140}](https://tex.z-dn.net/?f=h%20%3D%20%5Cfrac%7B0.0543%7D%7B9.8%20%2A%200.140%7D)
Answer:
460.52 s
Explanation:
Since the instantaneous rate of change of the voltage is proportional to the voltage in the condenser, we have that
dV/dt ∝ V
dV/dt = kV
separating the variables, we have
dV/V = kdt
integrating both sides, we have
∫dV/V = ∫kdt
㏑(V/V₀) = kt
V/V₀ = ![e^{kt}](https://tex.z-dn.net/?f=e%5E%7Bkt%7D)
Since the instantaneous rate of change of the voltage is -0.01 of the voltage dV/dt = -0.01V
Since dV/dt = kV
-0.01V = kV
k = -0.01
So, V/V₀ = ![e^{-0.01t}](https://tex.z-dn.net/?f=e%5E%7B-0.01t%7D)
V = V₀![e^{-0.01t}](https://tex.z-dn.net/?f=e%5E%7B-0.01t%7D)
Given that the voltage decreases by 90 %, we have that the remaining voltage (100 % - 90%)V₀ = 10%V₀ = 0.1V₀
So, V = 0.1V₀
Thus
V = V₀![e^{-0.01t}](https://tex.z-dn.net/?f=e%5E%7B-0.01t%7D)
0.1V₀ = V₀![e^{-0.01t}](https://tex.z-dn.net/?f=e%5E%7B-0.01t%7D)
0.1V₀/V₀ = ![e^{-0.01t}](https://tex.z-dn.net/?f=e%5E%7B-0.01t%7D)
0.1 = ![e^{-0.01t}](https://tex.z-dn.net/?f=e%5E%7B-0.01t%7D)
to find the time, t it takes the voltage to decrease by 90%, we taking natural logarithm of both sides, we have
㏑(0.01) = -0.01t
So, t = ㏑(0.01)/-0.01
t = -4.6052/-0.01
t = 460.52 s
Answer:
a=2 ok do it and ........
Explanation:
The five-step process for treating a muscle or joint injury such as an ankle sprain is called "P.R.I.C.E." which is short for Protection, Rest, Ice, Compression, and Elevation).